Problem: Simplify the following expression: $\dfrac{108p^4}{63p^4}$ You can assume $p \neq 0$.
Explanation: $ \dfrac{108p^4}{63p^4} = \dfrac{108}{63} \cdot \dfrac{p^4}{p^4} $ To simplify $\frac{108}{63}$ , find the greatest common factor (GCD) of $108$ and $63$ $108 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3$ $63 = 3 \cdot 3 \cdot 7$ $ \mbox{GCD}(108, 63) = 3 \cdot 3 = 9 $ $ \dfrac{108}{63} \cdot \dfrac{p^4}{p^4} = \dfrac{9 \cdot 12}{9 \cdot 7} \cdot \dfrac{p^4}{p^4} $ $\phantom{ \dfrac{108}{63} \cdot \dfrac{4}{4}} = \dfrac{12}{7} \cdot \dfrac{p^4}{p^4} $ $ \dfrac{p^4}{p^4} = \dfrac{p \cdot p \cdot p \cdot p}{p \cdot p \cdot p \cdot p} = 1 $ $ \dfrac{12}{7} \cdot 1 = \dfrac{12}{7} $